With the use of the recursive paraxial ray-trace procedure described by Moore [
J. Opt. Soc. Am. 61,
886 (
1971)] to examine the properties of the crystalline lens of the eye, several cases of false or nonconvergence of the series were discovered. Two cases are presented here.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
The corneal data are the same as those of the Gullstrand number 1 schematic eye, n is the refractive index, d is the surface separation, and R is the radius of curvature.
Iris or aperture stop.
Table 2
Ray-Trace Results for the Convergence Only, Checked by the Value of the Optical Invariant at the Back Surface of the Lensa
Z
ua
ha
ub
hb
n
H
0.0
−0.032225
0.882357
0.750103
2.688691
1.336000
−1.000000
1.0
−0.035853
0.848318
0.717714
3.422600
1.366240
−0.999488
2.0
−0.039481
0.810651
0.685325
4.124119
1.389760
−0.998381
3.0
−0.043109
0.769356
0.652936
4.793250
1.406560
−0.997211
4.0
−0.046736
0.724434
0.620548
5.429992
1.416640
−0.996357
5.0
−0.050364
0.675883
0.588159
6.034345
1.420000
−0.996047
6.0
−0.053992
0.623705
0.555770
6.606310
1.416640
−0.996357
7.0
−0.057620
0.567899
0.523381
7.145885
1.406560
−0.997211
8.0
−0.061247
0.508466
0.490992
7.653072
1.389760
−0.998381
9.0
−0.064875
0.445405
0.458604
8.127870
1.366240
−0.999488
10.0
−0.068503
0.378716
0.426215
8.570279
1.336000
−1.000000
n is the refractive index, and H is the optical invariant.
Table 3
Effect of Varying the Relative Amounts of c1 and c3 (Keeping Edge and Central Refractive Index Constant) on the Convergence of the Series Given by Eq. (5)
The corneal data are the same as those of the Gullstrand number 1 schematic eye, n is the refractive index, d is the surface separation, and R is the radius of curvature.
Iris or aperture stop.
Table 2
Ray-Trace Results for the Convergence Only, Checked by the Value of the Optical Invariant at the Back Surface of the Lensa
Z
ua
ha
ub
hb
n
H
0.0
−0.032225
0.882357
0.750103
2.688691
1.336000
−1.000000
1.0
−0.035853
0.848318
0.717714
3.422600
1.366240
−0.999488
2.0
−0.039481
0.810651
0.685325
4.124119
1.389760
−0.998381
3.0
−0.043109
0.769356
0.652936
4.793250
1.406560
−0.997211
4.0
−0.046736
0.724434
0.620548
5.429992
1.416640
−0.996357
5.0
−0.050364
0.675883
0.588159
6.034345
1.420000
−0.996047
6.0
−0.053992
0.623705
0.555770
6.606310
1.416640
−0.996357
7.0
−0.057620
0.567899
0.523381
7.145885
1.406560
−0.997211
8.0
−0.061247
0.508466
0.490992
7.653072
1.389760
−0.998381
9.0
−0.064875
0.445405
0.458604
8.127870
1.366240
−0.999488
10.0
−0.068503
0.378716
0.426215
8.570279
1.336000
−1.000000
n is the refractive index, and H is the optical invariant.
Table 3
Effect of Varying the Relative Amounts of c1 and c3 (Keeping Edge and Central Refractive Index Constant) on the Convergence of the Series Given by Eq. (5)